Global Conformal Invariance and Bilocal Fields with Rational Correlation Functions

Nikolov, Nikolay M.; Stanev, Yassen S.; Todorov, Ivan T.

Global Conformal Invariance and Bilocal Fields with Rational Correlation Functions

Authors

Nikolov, Nikolay M.

Stanev, Yassen S.

Todorov, Ivan T.

Description

The singular part of the \textit{operator product expansion} (OPE) of a pair of \textit{globally conformal invariant} (GCI) scalar fields $ϕ$ of (integer) dimension $d$ can be written as a sum of the 2-point function of $ϕ$ and $d-1$ bilocal conformal fields $V_ν(x_1, x_2)$ of dimension $(ν, ν)$, $ν= 1, ..., d-1$. As the correlation functions of $ϕ(x)$ are proven to be rational [6], we argue that the correlation functions of $V_ν$ can also be assumed rational. Each $V_ν(x_1, x_2)$ is expanded into local symmetric tensor fields of \textit{twist} (dimension minus rank) $2ν$. The case $d=2$, considered previously [5], is briefly reviewed and current work on the $d=4$ case (of a Lagrangean density in 4 space--time dimensions) is previewed.
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